In a joint statement, the secretaries of foreign affairs and the interior stopped short of shutting the country's southern border to the Hondurans, while making clear Mexico will enforce its immigration laws.

"In compliance with current national legislation, any person who enters the country in an irregular manner, will be rescued and subject to an administrative procedure and, where appropriate, will be returned to their country of origin, in a safe and orderly manner," reads the statement.

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About 3,000 Honduran nationals crossed from Honduras to Guatemala Monday, traveling together with the stated intent of seeking asylum in the United States. The caravan has since grown to over 4,000 people, according to a report by NBC News.

Mexico also assigned an extra 500 federal police officers to patrol its border with Guatemala ahead of the caravan's arrival.

Mexico's move is the latest in a series of actions by regional governments to separate themselves from the caravan, after Trump tweeted Tuesday that he informed Honduran President Juan Orlando Hernandez that "if the large Caravan of people heading to the U.S. is not stopped and brought back to Honduras, no more money or aid will be given to Honduras, effective immediately!"

Guatemalan authorities arrested a caravan organizer, Bartolo Fuentes, who is also a former Honduran lawmaker.

Honduran authorities released a statement urging "the Hondurans taking part in this irregular mobilization not to be used by a movement that is clearly political," reported Reuters.

And a senior Trump administration official told reporters at the White House Wednesday "this caravan did not happen organically."

Still, Mexico's response was tempered with instructions for migrants on how to legally enter and seek asylum in the country, "in adherence to a migration policy that respects the human rights of all migrants and international humanitarian law, recognizes the right of freedom of movement of persons and the right of any individual to seek refugee status."

Mexican authorities said incoming Central American migrants would be allowed to enter the country at official ports of entry if they have visas, or if they plan to claim asylum.

Mexican authorities said all incoming refuge and asylum seekers would remain in detention in migratory stations for a period of up to 90 days while their claims are processed.

Still, the southern border of Mexico is porous and thousands of Central American migrants cross it, legally or illegally, without getting stopped by Mexican authorities.

A record number of Central American families crossed the U.S.-Mexico border in September, according to a report by the Washington Post, after crossing into Mexico.

The growth in family crossings over the year has been driven in large part by increased emigration from Guatemala, and to a slightly lesser extent, from Honduras, according to figures released monthly by Customs and Border Protection (CBP).

CBP has yet to release official numbers for border apprehensions in September.

“On the news in Guatemala they are saying that you can get a work permit if you’re in a family, if you’re coming with your child, and that you’re going to be released,” said Henry Lucero, Phoenix field office director for U.S. Immigration and Customs Enforcement, in an interview with Arizona radio station KTAR Monday.

Adam Isacson, a Central American security expert at the Washington Office on Latin America, told The Hill in an email that there are many more push factors in play, including a drought in Guatemala's northern highlands, and drug cartel-fueled criminality.

But Isacson added that human smugglers play a role too, making pitches on social media and community radio that the Trump administration's reprieve on family separations at the U.S.-Mexico border is only temporary.

"[It's] unclear how much of this is a sense that family separation stopped but something more hardline could come soon, so we’re in a time between crackdowns," wrote Isacson.